WW2 Ciphers Part 3: Using A Daily Key

There are many stories about the attempts to get the enigma machines out of submarines or small boats throughout the war, but what they also wanted to get was the daily key books. These books had the settings for each day, i.e. how you rotated the wheels.

In the example above I used a daily key of {0,2,5,2}. At least one virtual wheel will turn each time a letter is ciphered, and that will produce a completely different wheel cipher byte. The table below shows what this looks like. The wheel cipher changes every letter.

Wheel Setting {0,2,5,2}
Plain text (Ascii)	Wheel Cipher	Cipher Text
69	135	194
108	172	192
32	185	153
77	215	154
97	237	140
99	151	244
104	57	81
111	171	196

This cipher works off of a fairly simple concept of Boolean exclusive-or (XOR) arithmetic. There are only four possible inputs. The function returns 0 if both inputs match, and 1 if they don't match, order doesn't matter.  Most computers store all data and numbers in binary, so it is possible to use this method on numbers of any size, you just do it one bit at a time.

Input		Output
A	B	A φ B
0	1	1
1	0	1
1	1	0
0	0	0

The principle of reciprocity is important, you can change the order of A and B and get the same results, the process of encrypting and decrypting is mathematically the same for this cipher. To encrypt we take plain text φ key = cipher text. Because of reciprocity we decipher by the formula key φ cipher text = plain text. You could even compute the key from the cipher text and plain text (plain text φ cipher text = key). The Tunny machine was completely cracked years before they even saw the machine or the wheels. A library of cipher texts and plain texts eventually allowed the code breakers to recreate the key sight unseen.

It's important to use a different wheel setting for each message. I know from my readings that messages which overlapped on the wheel settings were a key source when breaking the encryption. I figured I would have the most fun illustrating that concept by trying to break my own codes, so that will be the next post. I am working on a basic program for cracking using letter frequencies and I think it shows promise. Understanding this weakness will lead us to talk about the shortcoming of the daily key and why each message had an additional random message key.

Things to Try:

1. Download Roughy and cipher some messages.  https://drive.google.com/file/d/0B0RWL1ofCj90eHhPOHpxZkhxNEk/view?usp=sharing

2. Try this online XOR (exclusive-or) calculator.